We review the observational and theoretical results on the physics of microwave bursts that occur in the solar atmosphere. We particularly emphasize the advances made in burst physics over the last few years with the great improvement in spatial and time resolution especially with instruments like the NRAO three element interferometer, Westerbork Synthesis Radio Telescope and more recently the Very Large Array (VLA).We review the observations on pre-flare build-up of an active region at centimeter wavelengths. In particular we discuss the observations that in addition to the active region undergoing brightness and polarization changes on time scales of the order of an hour before a flare, there can be a change of the sense of polarization of a component of the relevant active region situated at the same location as the flare, implying the emergence of a flux of reverse polarity at coronal levels. The intensity distribution of cm-λ bursts is similar to that of soft X-ray and hard X-ray bursts. Indeed, it appears that the flaring behavior of the Sun at cm wavelengths is similar to that of some other cosmic transients such as flare stars and X-ray bursters.We discuss three distinct phases in the evolution of cm bursts, namely, impulsive phase, post-burst phase, and gradual rise and fall. The radiation mechanism for the impulsive phase of the microwave burst is gyrosynchrotron emission from mildly relativistic electrons that are accelerated near the energy release site and spiral in the strong magnetic field in the low corona. The details of the velocity distribution function of the energetic electrons and its time evolution are not known. We review the spectral characteristics for two kinds of velocity distribution, e.g., Maxwellian and Maxwellian with a power law tail for the energetic electrons. In the post-burst phase the energetic electrons are gradually thermalized. The thermal plasma released in the energy release region as well as the expanded parts of the overheated upper chromosphere may alter the emission mechanism. Thus, in the post-burst phase, depending on the average density and temperature of the thermal plasma, the emission mechanism may change from gyrosynchrotron to collisional bremsstrahlung from a thermal plasma. The gradual rise and fall (GFR) burst represents the heating of a flare plasma to temperatures of the order of 106 K, in association with a flare or an X-ray transient following a filament disruption.We discuss the flux density spectra of centimeter bursts. The great majority of the bursts have a single spectral maximum, commonly around 6 cm-λ The U-shaped signature sometimes found in cm-dcm burst spectrum of large bursts is believed to a be a reflection of only the fact that there are two different sources of burst radiation, one for cm-λ and the other for dcm-λ, with different electron energy distributions and different magnetic fields.Observations of fine structures with temporal resolutionof 10–100 ms in the intensity profiles of cm-λ bursts are described. The existence of such fine time structures imply brightness temperatures in burst sources of order 1015 K; their interpretation in terms of gyrosynchrotron measuring or the coherent interaction of upper hybrid waves excited by percipitating electron beams in a flaring loop is discussed.High spatial resolution observations (a few seconds of arc to ∼ 1″ arc) are discussed, with special reference to the one- and two-dimensional maps of cm burst sources. The dominance of one sense of circular polarization in some weak 6 cm bursts and its interpretation in terms of energetic electrons confined in an asymmetric magnetic loop is discussed. Two-dimensional snapshot maps obtained with the VLA show that multi-peak impulsive 6 cm burst phase radiation originates from several arcades of loops and that the burst source often occupies a substantial portion of the flaring loop, and is not confined strictly to the top of the loop. This phenomenon is interpreted in terms of the trapping of energetic electrons due to anomalous doppler resonance instability and the characteristic scale length of the magnetic field variation along the loop. The VLA observations also indicate that the onset of the impulsive phase of a 6 cm burst can be associated with the appearance of a new system of loops. The presence of two loop systems with opposite polarities or a quadrupole field configuration is reminiscent of flare models in which a current sheet develops in the interface between two closed loops.We provide an extensive review of the emission and absorption processes in thermal and non-thermal velocity distributions. Unlike the thermal plasma where absorption and emission are inter-related through Kirchoff's law, the radiation emitted from a small population of non-thermal electrons can be reabsorbed from the same electrons (self-absorption) or from the background (thermal) electrons through gyro-resonance absorption, and free-free absorption. We also suggest that the non-thermal electrons can be unstable and these instabilities can be the source of very high brightness temperature, fine structure (∼ 10 ms) pulsations.Finally in the last part of this review we present several microwave burst models-the magnetic trap model, the two-component model, thermal model and the flaring loop model and give a critical discussion of the strength and weakness of these models.